Math Modeling
Seminar
Predicting neural
network dynamics from graph structure
Dr. Katie
Morrison
Associate Professor of
Mathematical Sciences
University of Northern
Colorado
You may attend this
lecture in person at 2305 Gosnell Hall or virtually via
Zoom.
If you’d like to
attend virtually, you may register here for Zoom link.
Abstract:
Neural networks often
exhibit complex patterns of activity that are shaped by the intrinsic
structure of the network. For example, spontaneous sequences of neural
activity have been observed in cortex and hippocampus, and patterned
motor activity arises in central pattern generators for locomotion. In
this talk, we will focus on a simplified neural network model known as
Combinatorial Threshold-Linear Networks (CTLNs) in order to understand
how the pattern of neural connectivity, as encoded by a directed graph,
shapes the emergent nonlinear dynamics of the corresponding network. We
will see that important aspects of these dynamics are controlled by the
stable and unstable fixed points of the network, and show how these fixed
points can be determined via graph-based rules. We will then apply these
theoretical results to produce a model CPG for quadruped
gaits.
Speaker
Bio:
Dr. Katie Morrison is an
Associate Professor in the School of Mathematical Sciences at University
of Northern Colorado. She received her BA from Swarthmore College, double
majoring in mathematics and psychology, and her PhD in mathematics from
the University of Nebraska. Her dissertation work was in algebraic coding
theory, but she has since transitioned into mathematical neuroscience.
Dr. Morrison’s current research focus is on the mathematical theory and
analysis of neural networks and neural codes, using tools from algebra,
discrete mathematics, differential equations, and topology. This work has
been supported by an NIH BRAIN Initiative grant as well as two NSF
mathematical biology grants.
Read more
here.
Intended
Audience:
Undergraduates,
graduates, and experts. Those with interest in the topic.
The Math Modeling
Seminar will recur each week throughout the semester on the same day and
time. Find out more about upcoming speakers on the Mathematical Modeling Seminar Series
webpage.
To request an
interpreter, please visit myaccess.rit.edu